Compile and "True should be a machine-size real number..." Error

Question

I am trying to compile a little summation function. As far as I understand, because the built-in Sum function can also return NaN objects I have to make sure only numbers get out before returning.

X = Compile[{}, (
   result = Sum[i, {i, 10}];
   If[NumberQ[result], Return[result], Abort[]];
   )];

The problem is that I keep getting the following two warnings...

CompiledFunction::cfse: Compiled expression True should be a machine-size real number. CompiledFunction::cfex: Could not complete external evaluation at instruction 2; proceeding with uncompiled evaluation.

I guess the glitch is in the NumberQ function and its return type.

Any ideas on how to handle this issue correctly and effectively?

EDIT:

When I omit the check for numeric values while inserting a Return[] statement Mathematica falls back to the uncompiled version (warning: Compile::cret).

Answer 1

For the error handling use the compilers error handling mechanism:

cffail = Compile[{{x, _Real, 1}}, Exp[x], 
   "RuntimeOptions" -> {"RuntimeErrorHandler" -> Function[$Failed]}];
cffail[{1000.}]

The Function can be anything (Throw[..],...).

For the summation you could use Total in stead:

Compile[{{x, _Real, 1}}, Total[x]]

Answer 2

I'm having to read between the lines because you did not fully specify your problem, however I suspect that you need to use the third argument of Compile.

func =
  Compile[{{length}},
   (result = Sum[i^2, {i, length}]; If[NumberQ[result], result, Abort[]]),
   {{NumberQ[_], True | False}}
  ]

func[5]

55.

Answer 3

Are you definitely sure you need the error checking for NaN inside Compile? The error checking seems to generate very inefficient compiled code. It basically only calls MainEvaluate, so you gain nothing by compiling.

data = Range[1000];
func /@ data; // AbsoluteTiming
func1 /@ data; // AbsoluteTiming

(* ==> {0.1280073, Null} *)

(* ==> {0.0140008, Null} *)

func = 
  Compile[{{length}}, (result = Sum[i^2, {i, length}]; 
    If[NumberQ[result], result, Abort[]]), {{NumberQ[_], 
     True | False}}];
func1 = Compile[{{length, _Integer}}, Sum[i^2, {i, length}]];

data = Range[1000];
d1 = func /@ data; // AbsoluteTiming
d2 = func1 /@ data; // AbsoluteTiming
d1 == d2

(* ==> {0.1160067, Null} *)

(* ==> {0.0140008, Null} *)

(* ==> True *)

Needs["CompiledFunctionTools`"]
CompilePrint[func]
CompilePrint[func1]

(*
==> "
        1 argument
        1 Boolean register
        4 Integer registers
        7 Real registers
        Underflow checking off
        Overflow checking off
        Integer overflow checking on
        RuntimeAttributes -> {}

        R0 = A1
        I1 = 0
        R3 = 0.
        Result = R2

1   V17 = MainEvaluate[                                  2
Function[{length}, result = Sum[i , {i, length}]][ R0]]
2   B0 = MainEvaluate[ Function[{length}, NumberQ[result]][ R0]]
3   if[ !B0] goto 7
4   R5 = MainEvaluate[ Function[{length}, result][ R0]]
5   R2 = R5
6   goto 9
7   R1 = MainEvaluate[ Function[{length}, Abort[]][ R0]]
8   R2 = R1
9   Return
"
*)

(*
==> "
        1 argument
        9 Integer registers
        Underflow checking off
        Overflow checking off
        Integer overflow checking on
        RuntimeAttributes -> {}

        I0 = A1
        I3 = 0
        Result = I4

1   I4 = I3
2   I5 = I0
3   I7 = I3
4   goto 8
5   I6 = Square[ I7]
6   I8 = I4 + I6
7   I4 = I8
8   if[ ++ I7 < I5] goto 5
9   Return
"
*)

So my recommendation is to skip the check (what could generate the NaN in such a simple sum anyway?) or check for NaN values outside the compiled function.

Answer 4

I’m afraid your base assumption here is false, and the sum compiles much better without this call to NumberQ. See:

<< CompiledFunctionTools`;
func = Compile[{{length, _Integer}}, (
    Sum[i^2, {i, 1, length}]
    )];
CompiledFunctionTools`CompilePrint[func]

The output of CompilePrint shows that the sum is performed without any call to MainEvaluate, which you absolutely want to avoid if you to compile efficiently.